Planar coil and planar transformer
A planar coil includes a winding of N turns (N is an integer greater than or equal to 2). Letting ri(n) be a radius of an inner circumference of a winding portion at the nth turn (n is an integer greater than or equal to 1 and less than or equal to N) from the inner side; ro(n) be a radius of an outer circumference of the same; rmin be a radius of an inner circumference of the innermost winding portion; Wtotal be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the ri(n) and ro(n) are determined so as to minimize a value of A expressed by equation (1) when the rmin, Wtotla and D are given. A = ∑ n = 1 N ( log r o ( n ) r i ( n ) )  1 ( 1 )
The present invention relates to a planar coil and a planar transformer which have a winding that is formed by arranging a platelike conductor into a flatspiral shape.
BACKGROUND ARTPlanar coils and planar transformers are used as choke coils and transformers in switching power supplies and the like. The planar coils and planar transformers have a winding made of a patterned conductor that is formed by arranging a platelike conductor into a flatspiral shape. In the planar transformers, or the planar coils having a plurality of windings, the windings are stacked in a direction of thickness, with an insulating layer interposed between adjacent ones of the windings.
Among the planar coils and planar transformers, the ones that deliver relatively small output currents are formed by, for example, stacking a flatspiralshaped patterned conductor, an insulating layer, and a magnetic layer by thinfilm forming techniques such as sputtering. On the other hand, for the ones that deliver medium output currents, employed are: printed coils formed by stacking doublesided printed circuit boards with an insulating layer interposed therebetween, in which flatspiralshaped patterned conductors are formed on both surfaces of each printed circuit board by etching conductor layers disposed on both surfaces of the same; or coils formed by stacking flatspiralshaped patterned conductors with an insulating layer interposed therebetween, the patterned conductors being formed by diecutting a conductor plate. Those coils have a hole penetrating therethrough in a direction of thickness at a center portion of the patterned conductors. A magnetic substance such as an EEtype ferrite core is inserted in the hole.
Since such planar coils and planar transformers as mentioned above can be formed to have a smaller thickness, they are used for a compact and thin switching power supply and so on, in particular.
In recent years, because of decreased operating voltages and increased currents in ICs (Integrated Circuits) resulting from an increase in their scale of integration, it has been desired that a switching power supply be reduced in size and provide a large current. A loss caused by the resistance of a conductor in choke coils or transformers, i.e., the copper loss, increases in proportion to the square of the value of the current. For this reason, it is significant to reduce the resistance value of conductors in the planar coils or planar transformers which are used as choke coils or transformers.
Switching devices such as FETs (field effect transistors), one of major components of a switching power supply, have been reduced in both loss and size as the semiconductor technology has progressed. In contrast to this, it is difficult to reduce the size of magnetic components such as choke coils and transformers, the other major components of the switching power supply. For this reason, the ratio of the volume of the magnetic components to the volume of the entire switching power supply tends to increase. Although the magnetic components are under progress toward miniaturization, this depends largely on a fact that a switching frequency has become higher due to progress in the switching devices. If a higher switching frequency is achieved, it is possible to achieve a reduction in both size and loss of the core of the coil or the transformer. This, however, present a problem that the copper loss that is a loss in the conductor increases due to the skin effect.
Conventionally, most planar coils or planar transformers have a winding in which every perturn portion is constant in width. However, in this case, resistance becomes higher at the outer portions of the winding, which consequently causes an increase in the resistance of the entire winding.
To cope with this, Published Unexamined Japanese Patent Application (KOKAI) Heisei 5226155 discloses a technique of increasing the width of the winding of a coil with increasing distance from the center so that every portion of the winding has the same copper loss. In this technique, the width of each portion of the winding is determined by using complicated equations. Published Unexamined Japanese Patent Application (KOKAI) Heisei 737728 also discloses a technique of increasing the width of the winding of a coil with increasing distance from the center so that every portion of the winding has the same or substantially the same copper loss. In both of these techniques, a ratio between Ri and W, or Ri/W, where Ri represents the radius of an inner circumference of each perturn portion of the winding and W represents the width of each perturn portion of the winding, is made constant, thereby allowing the copper loss to be the same for every portion of the winding. This is intended to minimize the copper loss for the entire coil in a limited space.
However, it is not proved that the copper loss for the entire coil is minimized by making the Ri/W constant.
While the number of turns of the winding (the number of winding turns) in choke coils or transformers is determined in accordance with a ripple voltage and the input/output voltage ratio required of the switching power supply, and further with the power supply driving frequency, the shape and physical properties of the core, and so on, there are many cases in which an odd number of turns are required. Printed coils allow greater flexibility in design of windings as compared with coils employing wires. For example, for printed coils, it is possible to form a winding of a desired number of turns within a specific winding frame (or an area where to place a patterned conductor) by changing the width of the patterned conductor. Furthermore, for printed coils, a plurality of patterned conductors having the same pattern may be stacked and connected in parallel to each other using a throughhole or the like, thereby allowing adjustment of permissible current capacity.
Conventionally, for planar coils or planar transformers, the following four methods have been employed for forming a winding having an odd number of turns which is equal to or greater than three. A first method is to form the winding having a required odd number of turns by using one conductor layer that includes a patterned conductor of an odd number of turns. A second method is, as shown in, e.g., Published Unexamined Japanese Patent Application (KOKAI) Heisei 4113605, to connect an odd number of conductor layers in series to each other, each of the conductor layers including a patterned conductor of one turn. A third method is to connect a conductor layer including a patterned conductor of an even number of turns and a conductor layer including a patterned conductor of an odd number of turns in series to each other. A fourth method is, as shown in FIG. 6 to FIG. 9 of Published Unexamined Japanese Patent Application (KOKAI) Heisei 10163039, for example, to connect a conductor layer including a patterned conductor of the [even number+α] number of turns (where α is greater than zero and less than one) and a conductor layer including a patterned conductor of the [even number+(1−α)] number of turns in series to each other.
However, the aforementioned methods have the following problems. In the first method, one of terminals of the winding needs to be drawn out from the neighborhood of an inner edge of the patterned conductor. For this reason, in the first method, it is impossible to use a core typically employed for planar coils, that is, a core in which a connecting portion that connects the portion penetrating the winding (the socalled middle foot) to the portions facing the outer circumference of the winding (the socalled outer feet) has such a great width as to cover most part of the winding. To employ the first method, it is necessary to use a core in which the aforementioned connecting portion is small in width so as not to contact with the terminal of the winding to be drawn out from the neighborhood of the inner edge of the patterned conductor. In this case, to secure a sufficient crosssectional area of the core to avoid saturation of a magnetic flux, it is necessary to increase the thickness of the core. Thus, it is difficult for the first method to make the planar coils or planar transformers smaller in thickness.
In the second method, conductor layers as many as the number of turns required have to be stacked, which presents a problem that the planar coil or the planar transformer becomes greater in thickness. In addition, in the second method, connecting portions required for connecting an odd number of conductor layers in series to each other increase in number with increasing number of turns required. For example, forming a winding of five turns requires four connecting portions other than the terminals. This necessitates a wide area in the planar coil or the planar transformer for accommodating the connecting portions. Additionally, the second method allows a low degree of flexibility in designing the number of conductor layers because the number of conductor layers must coincide with the number of turns of the winding. For example, to form a winding of five turns, the number of conductor layers must be set in fivelayer increments. In this case, for example, to increase the number of conductor layers so as to increase current capacity, the number of conductor layers can only be made equal to a multiple of five. It is therefore impossible to provide, for example, eight or twelve layers to achieve a desired current capacity.
For the third and fourth methods, the patterned conductors in the two conductor layers can be wound in directions opposite to each other to electrically connect the inner ends of the two patterned conductors to each other. This makes it possible to draw out the two terminals of the winding from the outer ends of the two patterned conductors. Thus, in the third and fourth methods, both terminals of the winding can be disposed outside the core, and this allows use of a core that is small in thickness and has a wide connecting portion between the middle foot and the outer feet. Furthermore, in the third and fourth methods, it is possible to design the number of conductor layers in twolayer increments, which allows a high degree of flexibility in designing the number of conductor layers.
Third and fourth methods, however, cause great differences between portions of the patterned conductor in width, resulting in variations of the current density from portion to portion of the winding. For this reason, the third and fourth methods cannot allow an optimum design of a patterned conductor from the viewpoint of reducing loss.
DISCLOSURE OF THE INVENTIONIt is a first object of the invention to provide a planar coil and a planar transformer in which a winding is configured to minimize a loss in a limited space.
Additionally, it is a second object of the invention to provide a planar coil and a planar transformer having a winding of an odd number of turns and allowing a reduction in thickness, great flexibility in designing the number of conductor layers, and a reduction in loss.
A first planar coil of the invention comprises a winding formed by arranging a conductor into a flatspiral shape, the winding including winding portions of N turns (N is an integer greater than or equal to two), wherein: letting r_{i}(n) be a radius of an inner circumference of a winding portion at the n^{th }turn (n is an integer greater than or equal to one and less than or equal to N) from the inner side; r_{o}(n) be a radius of an outer circumference of the same; r_{min }be a radius of an inner circumference of the innermost winding portion; W_{total }be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize a value of A expressed by equation (1) when the r_{min}, W_{total }and D are given:
where r_{i}(1)=r_{min}, r_{i}(n+1)−r_{o}(n)=D, and r_{o}(N)−r_{i}(1)=W_{total}.
In the first planar coil of the invention, by setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A given by the equation (1), the resistance value of the entire winding becomes minimum, which results in a minimized loss in the entire winding. In the present application, a winding portion refers to a portion of the entire winding, the portion corresponding to one turn.
In the first planar coil of the invention, a plurality of the windings may be provided, and the plurality of the windings may be stacked in a direction of thickness with an insulating layer disposed between adjacent ones, and connected in parallel or in series to each other.
A first planar transformer of the invention comprises a plurality of windings each formed into a flat shape and stacked in a direction of thickness, and an insulating layer disposed between adjacent ones of the windings, a part of the plurality of windings serving as a primary winding and another part of the plurality of windings serving as a secondary winding, wherein:
at least one of the plurality of windings includes winding portions of N turns (N is an integer greater than or equal to two), the winding portions being formed by arranging a conductor into a flatspiral shape, and
letting r_{i}(n) be a radius of an inner circumference of a winding portion at the n^{th }turn (n is an integer greater than or equal to one and less than or equal to N) from the inner side; r_{o}(n) be a radius of an outer circumference of the same; r_{min }be a radius of an inner circumference of the innermost winding portion; W_{total }be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize a value of A expressed by equation (1) when the r_{min}, W_{total }and D are given:
where r_{i}(1)=r_{min}, r_{i}(n+1)−r_{o}(n)=D, and r_{o}(N)−r_{i}(1)=W_{total}.
In the first planar transformer of the invention, by setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A given by the equation (1), the resistance value of the entire winding becomes minimum, which results in a minimized loss in the entire winding.
A second planar coil of the invention has a winding of an odd number of turns, the winding being formed of a conductor, the planar coil comprising: an insulating layer; a first conductor layer including a first patterned conductor formed by arranging a conductor into a flatspiral shape; and a second conductor including a second patterned conductor formed by arranging a conductor into a flatspiral shape, the second conductor layer being adjacent to the first conductor layer via the insulating layer, wherein:

 the first patterned conductor and the second patterned conductor each have winding portions of N (N is an integer greater than or equal to one) plus one turns, and
the innermost winding portions of the first and second patterned conductors are connected in parallel to each other, thereby allowing the first patterned conductor and the second patterned conductor to form the winding of 2N+1 turns.
In the second planar coil of the invention, the innermost winding portions of the first and second patterned conductors are connected in parallel to each other so as to form a conductive path corresponding to one turn of the winding. On the other hand, the other winding portions of the first and second patterned conductors form a conductive path corresponding to 2N turns. In the present invention, the first patterned conductor and the second patterned conductor may be formed into the same pattern in terms of width. In the present invention, the conductive path corresponding to one turn that is formed by the innermost winding portions of the first and second patterned conductors is twice as thick as the other conductive path. However, by adjusting the width thereof, it is possible to reduce the resistance value of the entire winding of 2N+1 turns, and to thereby reduce the loss of the entire winding. The present invention covers not only the case where the first conductor layer and the second conductor layer are adjacent to each other via the insulating layer, but also the case where the first conductor layer and the second conductor layer are adjacent to each other via the insulating layer and another layer.
In the second planar coil of the invention, the innermost winding portion of each of the first and second patterned conductors may have a width that is substantially half the width of another winding portion. In this case, the conductive path corresponding to one turn that is formed by the innermost winding portions of the first and second patterned conductors is twice as thick as the other conductive path. However, since the width thereof is substantially half that of the other conductive path, the crosssectional area of the same is substantially equal to that of the other conductive path. Accordingly, a current density is uniformalized for every portion of the winding of 2N+1 turns, and a loss in the winding is thereby reduced.
In the present application, a winding portion refers to a portion of each patterned conductor, the portion corresponding to one turn. In addition, in the present application, “substantially half” is intended to include an exactly half value and also other values that contain tolerances, such as a rounding error in design or an error in manufacture, on the exactly half value.
In the second planar coil of the invention, in the first patterned conductor and the second patterned conductor, letting r_{i}(n) be a radius of an inner circumference of a winding portion at the n^{th }turn (n is an integer greater than or equal to 1 and less than or equal to N+1) from the inner side; r_{o}(n) be a radius of an outer circumference of the same; r_{min }be a radius of an inner circumference of the innermost winding portion; W_{total }be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) may be determined so as to minimize a value of A expressed by equation (5) when the r_{min}, W_{total }and D are given:
where K(1)=0.5; K(n)=2 when n≧2; r_{i}(1)=r_{min}; r_{i}(n+1)−r_{o}(n)=D; and r_{o}(N+1)−r_{i}(1)=W_{total}.
In this way, by setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A given by the equation (5), the resistance value of the entire winding becomes minimum, which results in a minimized loss in the entire winding.
In the second planar coil of the invention, a plurality of sets of the insulating layer, the first conductor layer and the second conductor layer may be stacked in a direction of thickness, with the windings of the respective sets connected in parallel to each other.
A second planar transformer of the invention has a primary winding and a secondary winding, each being formed of a conductor arranged into a flat shape, wherein:
at least one of the primary winding and the secondary winding comprises: a first conductor layer including a first patterned conductor formed by arranging a conductor into a flatspiral shape; and a second conductor including a second patterned conductor formed by arranging a conductor into a flatspiral shape, the second conductor layer being adjacent to the first conductor layer via an insulating layer,
the first patterned conductor and the second patterned conductor each have winding portions of N (N is an integer greater than or equal to one) plus one turns, and
the innermost winding portions of the first and second patterned conductors are connected in parallel to each other, thereby allowing the first patterned conductor and the second patterned conductor to form a winding of 2N+1 turns.
In the second planar transformer of the invention, the innermost winding portions of the first and second patterned conductors are connected in parallel to each other so as to form a conductive path corresponding to one turn of the winding. On the other hand, the other winding portions of the first and second patterned conductors form a conductive path corresponding to 2N turns. In the present invention, the first patterned conductor and the second patterned conductor may be formed into the same pattern in terms of width. In the present invention, the conductive path corresponding to one turn that is formed by the innermost winding portions of the first and second patterned conductors is twice as thick as the other conductive path. However, by adjusting the width thereof, it is possible to reduce the resistance value of the entire winding of 2N+1 turns, and to thereby reduce a loss in the entire winding. The present invention covers not only the case where the first conductor layer and the second conductor layer are adjacent to each other via the insulating layer, but also the case where the first conductor layer and the second conductor layer are adjacent to each other via the insulating layer and another layer.
In the second planar transformer of the invention, the innermost winding portion of each of the first and second patterned conductors may have a width that is substantially half the width of another winding portion. In this case, the conductive path corresponding to one turn that is formed by the innermost winding portions of the first and second patterned conductors is twice as thick as the other conductive path. However, since the width thereof is substantially half that of the other conductive path, the crosssectional area of the same is substantially equal to that of the other conductive path. Accordingly, a current density is uniformalized for every portion of the winding of 2N+1 turns, and a loss in the winding is thereby reduced.
In the second planar transformer of the invention, in the first patterned conductor and the second patterned conductor, letting r_{i}(n) be a radius of an inner circumference of a winding portion at the n^{th }turn (n is an integer greater than or equal to 1 and less than or equal to N+1) from the inner side; r_{o}(n) be a radius of an outer circumference of the same; r_{min }be a radius of an inner circumference of the innermost winding portion; W_{total }be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) may be determined so as to minimize the value of A expressed by equation (5) when the r_{min}, and D are given:
where K(1)=0.5; K(n)=2 when n≧2; r_{i}(1)=r_{min}; r_{i}(n+1)−r_{o}(n)=D; and r_{o}(N+1)−r_{i}(1)=W_{total}.
In this way, by setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A given by the equation (5), the resistance value of the entire winding becomes minimum, which results in a minimized loss in the entire winding.
Other objects, features and advantages of the invention will become sufficiently clear from the following description.
Embodiments of the invention will now be described in detail with reference to the drawings.
[First Embodiment]
Reference is now made to FIG. 1 and
The winding 11 is made of a patterned conductor that is formed by arranging a platelike conductor, including a foillike conductor, into a flatspiral shape. The conductor may be copper, for example. Throughholes 12 that penetrate the winding 11 and the insulating layer 10 are formed at positions of both ends of the winding 11. For example, the throughholes 12 are used as terminals of the planar coil or as connecting portions for connecting a plurality of planar coils in parallel or in series to each other.
For example, the planar coil according to the embodiment may be fabricated by etching a conductor layer formed on one surface of an insulating substrate of a printed circuit board, or by stamping a conductor plate. Alternatively, the planar coil may also be fabricated by forming a patterned conductor on one surface of the insulating substrate using a thinfilm forming technique such as a sputtering method.
In the planar coil according to the embodiment, the winding 11 includes winding portions of N turns. Letting r_{i}(n) be the radius of the inner circumference (hereinafter referred to as inner radius) of a winding portion at the n^{th }turn (n is an integer greater than or equal to one and less than or equal to N) from the inner side; r_{o}(n) be the radius of the outer circumference (hereinafter referred to as outer radius) of the same; r_{min }be the inner radius of the innermost winding portion; W_{total }be a difference between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize the value of A given by the following equation (1) when the r_{min}, W_{total }and D are given:
where r_{i}(1)=r_{min}, r_{i}(n+1)−r_{o}(n)=D, and r_{o}(N)−r_{i}(1)=W_{total}. Additionally, logx is a natural logarithm of x.
By setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A given by the equation (1), the resistance value of the entire winding 11 becomes minimum, which results in a minimized loss in the entire winding 11. This will be discussed in more detail below.
First, let us consider a ringshaped patterned conductor of thickness t, inner radius r, and outer radius r+dr. The resistance value of this patterned conductor may be represented by (2πr×ρ)/(t×dr) if the width dr is sufficiently infinitesimal. Here, ρ is the volume resistivity of the conductor. Therefore, the conductance of the patterned conductor, i.e., the reciprocal of the resistance value, is (t×dr)/(2πr×ρ).
The ringshaped patterned conductor with inner radius r_{i }and outer radius r_{o }is considered to be equivalent to a plurality of ringshaped patterned conductors connected in parallel to each other, each of the conductors having an infinitesimal width dr as mentioned above. Therefore, the conductance of the ringshaped patterned conductor of thickness t, inner radius r_{i}, and outer radius r_{o }can be determined by integrating the (t×dr)/(2πr×ρ) over the range from r_{i }to r_{o }as shown in the following equation (2).
The resistance value R of the ringshaped patterned conductor of thickness t, inner radius r_{i}, and outer radius r_{o }is the reciprocal of the conductance of this patterned conductor, and therefore is expressed by the following equation (3):
The winding 11 made up of winding portions of N turns is considered to be equivalent to the N number of ringshaped patterned conductors (winding portions) connected in series to each other. Therefore, the resistance value R_{total }of the entire winding 11 of N turns is expressed by the following equation (4):
Therefore, setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A expressed by the aforementioned equation (1) can minimize the resistance value of the entire winding 11 when the inner radius r_{min }of the innermost winding portion, a difference W_{total }between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion, and a distance D between winding portions at adjacent turns are given.
Values of the r_{i}(n) and r_{o}(n) to minimize the value of A are difficult to find analytically, but can be determined through numerical calculation using a computer.
Now, explained below are working examples of the planar coil according to the present embodiment and the results of comparison of calculated resistance values between planar coils of the working examples and comparative examples.
A planar coil of a first working example includes, as shown in FIG. 1 and
For each of the planar coils of the first working example, the first comparative example and the second comparative example, the width W(n) of a winding portion at each turn and the resistance value R_{total }of the entire winding are as shown in the following table.
As can be seen from the table above, according to the planar coil of the first working example, the resistance value R_{total }of the entire winding is reduced by 10.63% compared with the planar coil of the first comparative example, and by 0.38% compared with the planar coil of the second comparative example.
Although not shown, a planar coil according to a second working example includes the winding 11 of four turns. For this planar coil, copper was used as the conductor constituting the winding 11, thickness t of the conductor was set to 0.06 mm, inner radius r_{min }of the innermost winding portion was set to 3 mm, difference W_{total }between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion was set to 5 mm, and distance D between winding portions at adjacent turns was set to 0.2 mm. For this planar coil, values of the inner radius r_{i}(n) and the outer radius r_{o}(n) of a winding portion at each turn to minimize the value of A expressed by the aforementioned equation (1), as well as the resistance value R_{total }of the entire winding 11, were determined through numerical calculation using a computer.
A planar coil of a third comparative example includes a winding of four turns, and is constant in width W(n) of a winding portion at every turn. The other conditions of the planar coil of the third comparative example are the same as those of the planar coil of the second working example.
A planar coil of a fourth comparative example includes a winding of four turns, and is constant in the ratio of the inner radius r_{i}(n) to the width W(n), i.e., r_{i}(n)/W(n), of a winding portion at each turn. The other conditions of the planar coil of the fourth comparative example are the same as those of the planar coil of the second working example.
For each of the planar coils of the second working example, the third comparative example and the fourth comparative example, the width W(n) of a winding portion at each turn and the resistance value R_{total }of the entire winding are as shown in the following table.
As can be seen from the table above, the planar coil of the second working example has a resistance value R_{total }of the entire winding reduced by 6.31% compared with the planar coil of the third comparative example, and by 0.05%, although slight, compared with the planar coil of the fourth comparative example.
As described above, in the planar coil according to the present embodiment, since the r_{i}(n) and r_{o}(n) are set so as to minimize the value of A expressed by the equation (1), it is possible to minimize the resistance value of the entire winding 11. Thus, according to the embodiment, it is possible to arrange the winding 11 so as to minimize loss in a limited space, and to thereby reduce a loss caused by the resistance of the conductor. Furthermore, the planar coil according to the embodiment can attain reduction in a resistance value of the entire winding 11 as compared with a planar coil which is constant in width W(n) of a winding portion at every turn or with a planar coil which is constant in the ratio of the inner radius r_{i}(n) to the width W(n), i.e., r_{i}(n)/W(n), of a winding portion at each turn.
[Second Embodiment]
Now, description will be given of a configuration of a planar coil according to a second embodiment of the invention.
As shown in
Each of the windings 21 to 24 is made of a patterned conductor that is formed by arranging a platelike conductor, including a foillike conductor, into a flatspiral shape. Additionally, each of the windings 21 to 24 is a winding of N turns (N is an integer greater than or equal to two). By way of example,
As shown in FIG. 8 and
As shown in FIG. 9 and
As shown in
In such a manner, the windings 21 and 23 are connected in parallel to each other, and the windings 22 and 24 are also connected in parallel to each other. The windings 21/23 are connected in series to the windings 22/24. Accordingly, when each of the windings 21 to 24 has five turns, the windings 21 to 24 form a winding of 10 turns.
For example, as shown in
Additionally, as shown in
The windings 21 and 22 may be formed by etching conductor layers formed on both surfaces of an insulating substrate of a doublesided printed circuit board. The windings 23 and 24 may be formed in the same manner. In this case, the stacked body composed of the windings 21 to 24 and the insulating layers 20 may be fabricated by stacking the two doublesided printed circuit boards via the insulating layer 20. Alternatively, the stacked body composed of the windings 21 to 24 and the insulating layers 20 may be fabricated by: forming the windings 22 and 23 by etching conductor layers on a doublesided printed circuit board, then stacking singlesided printed circuit boards on top and bottom of the doublesided printed circuit board via insulating layers, and then etching conductor layers of the two exposed singlesided printed circuit boards to thereby form the windings 21 and 24. Alternatively, the stacked body composed of the windings 21 to 24 and the insulating layers 20 may be fabricated by stamping a conductor plate to form the windings 21 to 24, and then by stacking the windings via insulating layers made of a material such as polyimide film. Alternatively, the stacked body composed of the windings 21 to 24 and the insulating layers 20 may be fabricated by using a thinfilm forming technique such as a sputtering method.
In the planar coil according to the present embodiment, each of the windings 21 to 24 includes winding portions of N turns, like the winding 11 of the first embodiment. Letting r_{i}(n) be the inner radius of a winding portion at the n^{th }turn from the inner side; r_{o}(n) be the outer radius of the same; r_{min }be the inner radius of the innermost winding portion; W_{total }be a difference between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize the value of A given by the equation (1) when the r_{min}, W_{total }and D are given.
The remainder of the configuration, functions and effects of the present embodiment are the same as those of the first embodiment.
[Third Embodiment]
Now, description will be given of a configuration of a planar transformer according to a third embodiment of the invention.
As shown in
As shown in FIG. 16 and
On the other hand, as shown in FIG. 17 and
As shown in
As shown in
As shown in FIG. 17 and
For example, as shown in
Additionally, as shown in
The windings 31 and 32 may be formed by etching conductor layers formed on both surfaces of an insulating substrate of a doublesided printed circuit board. The windings 33 and 34 may be formed in the same manner. In this case, the stacked body composed of the windings 31 to 34 and the insulating layers 30 may be fabricated by stacking the two doublesided printed circuit boards via the insulating layer 30. Alternatively, the stacked body composed of the windings 31 to 34 and the insulating layers 30 may be fabricated by: forming the windings 32 and 33 by etching conductor layers on a doublesided printed circuit board, then stacking singlesided printed circuit boards on top and bottom of the doublesided printed circuit board via insulating layers, and then etching conductor layers of the two exposed singlesided printed circuit boards to thereby form the windings 31 and 34. Alternatively, the stacked body composed of the windings 31 to 34 and the insulating layers 30 may be fabricated by stamping a conductor plate to form the windings 31 to 34, and then by stacking the windings via insulating layers made of a material such as polyimide film. Alternatively, the stacked body composed of the windings 31 to 34 and the insulating layers 30 may be fabricated by using a thinfilm forming technique such as a sputtering method.
In the planar transformer according to the embodiment, one of the windings 31/34 and 32/33 serves as a primary winding and the other as a secondary winding.
In the planar transformer according to the embodiment, each of the windings 32 and 33 includes winding portions of N turns, like the winding 11 of the first embodiment. Letting r_{i}(n) be the inner radius of a winding portion at the n^{th }turn from the inner side; r_{o}(n) be the outer radius of the same; r_{min }be the inner radius of the innermost winding portion; W_{total }be a difference between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize the value of A given by the equation (1) when the r_{min}, W_{total }and D are given.
The remainder of the configuration, functions and effects of the present embodiment are the same as those of the first embodiment.
In the first to third embodiments, the number of turns and the number of windings can be set to any number.
Additionally, in the first to third embodiments, the winding may be formed of a conductor other than plateshaped ones, and may be formed of a rounded wire conductor, for example.
As described in the foregoing, in the first to third embodiments, by setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A expressed by the equation (1), it is possible to arrange the winding so as to minimize loss in a limited space, and to thereby reduce a loss caused by the resistance of the conductor.
[Fourth Embodiment]
Reference is now made to
The planar coil according to the embodiment comprises: a rectangular plateshaped insulating layer 40; a first conductor layer 41 formed on one surface (top surface) of the insulating layer 40; and a second conductor layer 42 formed on the other surface (bottom surface) of the insulating layer 40. Thus, the first conductor layer 41 and the second conductor layer 42 are adjacent to each other via the insulating layer 40.
In the vicinity of one of side portions of the insulating layer 40, there is provided a terminal area 40b in which terminals of the windings are disposed. There is formed a circular hole 40a at the center of part of the insulating layer 40 excluding the terminal area 40b. The hole 40a is configured such that a core can be inserted therein.
As shown in
The planar coil according to the present embodiment may be fabricated by etching conductor layers formed on both surfaces of an insulating substrate of a doublesided printed circuit board, or by stamping a conductor plate. Alternatively, the planar coil may also be fabricated by using a thinfilm forming technique such as a sputtering method.
The first patterned conductor 41a and the second patterned conductor 42a each include winding portions of N (N is an integer greater than or equal to one) plus one turns. The present embodiment is configured so that N=1. That is, the first patterned conductor 41a and the second patterned conductor 42a each include winding portions of two turns.
The first patterned conductor 41a and the second patterned conductor 42a are wound in opposite directions. That is, as shown in
As shown in
As shown in
At the lefthand position in the terminal area 40b, there is formed a throughhole 45 that penetrates the terminal layer 43, the insulating layer 40, and the outer end of the second patterned conductor 42a. The terminal layer 43 and the outer end of the second patterned conductor 42a are electrically connected to each other via the throughhole 45.
At the righthand position in the terminal area 40b, there is formed a throughhole 46 that penetrates the outer end of the first patterned conductor 41a, the insulating layer 40, and the terminal layer 44. The outer end of the first patterned conductor 41a and the terminal layer 44 are electrically connected to each other via the throughhole 46.
As shown in FIG. 21 and
In the present embodiment, as shown in FIG. 21 and
In the present embodiment, as shown in FIG. 21 and
In addition, according to the embodiment, the two conductor layers 41 and 42 can form a winding of three turns. Furthermore, according to the embodiment, two terminals of the winding can be drawn out from the outer ends of the two patterned conductors 41a and 42a. Thus, both terminals of the winding can be disposed outside a wide core, which makes it possible to use a core small in thickness and having a wide connecting portion between the middle foot and the outer feet. From the foregoing, the embodiment can attain a planar coil of smaller thickness.
Furthermore, according to the embodiment, the number of layers of the conductor layers 41 and 42 can be designed in twolayer increments, which allows a higher degree of flexibility in designing the number of layers of the conductor layers 41 and 42.
[Fifth Embodiment]
Reference is now made to FIG. 25 and
The configuration of the planar coil according to the embodiment is the same as that of the planar coil according to the fourth embodiment except that the patterned conductors 41a and 42a are different in shape.
According to the planar coil of the embodiment, in the first patterned conductor 41a and the second patterned conductor 42a, letting r_{i}(n) be the radius of the inner circumference of a winding portion at the n^{th }turn (n is an integer greater than or equal to 1 and less than or equal to N+1) from the inner side; r_{o}(n) be the radius of the outer circumference of the same; r_{min }be the radius of the inner circumference of the innermost winding portion; W_{total }be a difference between the radius of the outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize the value of A given by the following equation (5) when the r_{min}, W_{totla }and D are given: 4
where K(1)=0.5; K(n)=2 when n≧2; r_{i}(1)=r_{min}; r_{i}(n+1)−r_{o}(n)=D; and r_{o}(N+1)−r_{i}(1)=W_{total}. Additionally, logx is a natural logarithm of x.
By setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A given by the equation (5), the resistance value of the entire winding of 2N+1 turns becomes minimum, which results in a minimized loss in the entire winding. This will be discussed in more detail below.
First, let us consider a ringshaped patterned conductor of thickness t, inner radius r, and outer radius r+dr. The resistance value of the patterned conductor may be represented by (2πr×ρ)/(t×dr) if the width dr is sufficiently infinitesimal. Here, ρ is the volume resistivity of the conductor. Therefore, the conductance of the patterned conductor, i.e., the reciprocal of the resistance value, is (t×dr)/(2πr×ρ).
The ringshaped patterned conductor with inner radius r_{i }and outer radius r_{o }is considered to be equivalent to a plurality of ringshaped patterned conductors connected in parallel to each other, each of the conductors having an infinitesimal width dr as mentioned above. Therefore, the conductance of the ringshaped patterned conductor of thickness t, inner radius r_{i}, and outer radius r_{o }can be determined by integrating the (t×dr)/(2πr×ρ) over the range from r_{i }to r_{o }as shown in the following equation (6).
The resistance value R of the ringshaped patterned conductor of thickness t, inner radius r_{i}, and outer radius r_{o }is the reciprocal of the conductance of the patterned conductor, and therefore is expressed by the following equation (7):
Here, it is set that 2πρ/t=B. The resistance value R of the conductive path corresponding to one turn that is formed by the innermost winding portions of the first and second patterned conductors 41a and 42a is expressed by the following equation (8):
On the other hand, the sum R of a resistance value per turn of another winding portion of the first patterned conductor 41a and a resistance value per turn of another winding portion of the second patterned conductor 42a is expressed by the following equation (9):
Therefore, the resistance R_{total }of the entire winding of 2N+1 turns is expressed by the following equation (10):
Accordingly, in the first patterned conductor 41a and the second patterned conductor 42a, setting the r_{i}(n) and r_{o}(n) so as to minimize the value of A expressed by the aforementioned equation (5) can minimize the resistance value of the entire winding of 2N+1 turns when the inner radius r_{min }of the innermost winding portion, a difference W_{total }between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion, and a distance D between winding portions at adjacent turns are given.
Values of the r_{i}(n) and r_{o}(n) to minimize the value of A are difficult to find analytically, but can be determined through numerical calculation using a computer.
The present embodiment is configured so that the first patterned conductor 41a and the second patterned conductor 42a form a winding of three turns, by setting N=1.
According to the planar coil of the present embodiment, it is possible to minimize the resistance value of the entire winding because the r_{i}(n) and r_{o}(n) are set so as to minimize the value of A expressed by the equation (5). The embodiment thus makes it possible to arrange the winding so as to minimize loss in a limited space, and to thereby reduce a loss caused by resistance of the conductor.
The remainder of the configuration, functions and effects of the present embodiment are the same as those of the fourth embodiment.
Now, explained below are an example of the planar coil according to the fourth embodiment (hereinafter referred to as a third working example) and an example of the planar coil according to the fifth embodiment (hereinafter referred to as a fourth working example), and the results of comparison of calculated resistance values between planar coils of the working examples and those of two comparative examples.
For each of the planar coils of the third working example, the fourth working example, the fifth comparative example and the sixth comparative example, copper was used as the conductor constituting the winding, thickness t of the conductor was set to 0.06 mm, the inner radius r_{min }of the innermost winding portion was set to 6.4 mm, a difference W_{total }between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion was set to 5.1 mm, and a distance D between winding portions at adjacent turns was set to 0.2 mm. Under these conditions, values of the inner radius r_{i}(n) and the outer radius r_{o}(n) for a winding portion at each turn and a resistance value R_{total }of the entire winding were determined for each planar coil. The volume resistivity of the copper was set to 1.72×10^{−8 }(Ωm). The width r_{o}(n)−r_{i}(n) of a winding portion at each turn is hereinafter expressed as W(n).
For each of the planar coils of the third working example, the fourth working example and the fifth comparative example, the width W(n) of a winding portion at each turn and the resistance value R_{total }of the entire winding are as shown in the following table. In the table, the first conductor layer is referred to as “layer A” and the second conductor layer is referred to as “layer B”. According to the planar coil of the sixth comparative example, the ratio of the width of the portion forming the conductive path corresponding to two turns in W_{total }to the width of the portion forming the conductive path corresponding to one turn in W_{total }is the same as that of the fifth comparative example. Thus, in principle, the resistance value is equivalent to that of the fifth comparative example.
As can be seen from the table above, for the planar coil of the third working example, the resistance value R_{total }of the entire winding is reduced by 8.71% compared with the planar coil of the fifth comparative example. For the planar coil of the fourth working example, the resistance value R_{total }of the entire winding is reduced by 10.45% compared with the planar coil of the fifth comparative example.
In the third working example, the width W(1) of the inner winding portion is 0.5 times the width W(2) of the outer winding portion. As for the fourth working example, the width W(n) of a winding portion at each turn being determined so as to minimize the value of A expressed by the equation (5), in the aforementioned example the width W(1) of the inner winding portion is 0.37 times the width W(2) of the outer winding portion. However, the resistance value R_{total }of the entire winding can be made lower than that of the planar coil of the fifth comparative example even when the ratio of the width W(1) of the inner winding portion to the width W(2) of the outer winding portion, i.e., W(1)/W(2), is not equal to 0.5 or 0.37. This will be discussed with reference to FIG. 31 and FIG. 32.
The range of W(1)/W(2) in which the aforementioned ratio of resistance values becomes less than or equal to one varies depending on the values of r_{min}, W_{total}, and D. For example, consider the case where r_{min }is 3 mm with the other conditions being the same as those employed for determining the plot of FIG. 31. Additionally, as a comparative example for this case, consider a case where r_{min }is 3 mm with the other conditions being the same as those of the fifth comparative example. The ratio of the resistance value R_{total }of the entire winding of this case to the resistance value R_{total }of the entire winding of the comparative example, as the W(1)/W(2) is varied, is plotted in FIG. 32. In this case, from
According to the invention, it is thus possible to reduce the resistance value R_{total }of the entire winding in such a wide range as shown in
[Sixth Embodiment]
Reference is now made to
The planar coil according to the present embodiment is configured so that N=2. That is, the first patterned conductor 41a and the second patterned conductor 42a each include winding portions of three turns. Then, the first patterned conductor 41a and the second patterned conductor 42a form a winding of 2N+1=5 turns. In each of the first patterned conductor 41a and the second patterned conductor 42a, the innermost winding portion is substantially half the width of the other winding portions. The other winding portions have constant widths. The remainder of the configuration, functions and effects of this embodiment are the same as those of the fourth embodiment.
[Seventh Embodiment]
Reference is now made to FIG. 37 and
The configuration of the planar coil according to the present embodiment is the same as that of the planar coil according to the sixth embodiment except that the patterned conductors 41a and 42a are different in shape.
According to the planar coil of the present embodiment, like that of the fifth embodiment, in the first patterned conductor 41a and the second patterned conductor 42a, letting r_{i}(n) be the radius of the inner circumference of a winding portion at the n^{th }turn (n is an integer greater than or equal to 1 and less than or equal to N+1) from the inner side; r_{o}(n) be the radius of the outer circumference of the same; r_{min }be the radius of the inner circumference of the innermost winding portion; W_{total }be a difference between the radius of the outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the r_{i}(n) and r_{o}(n) are determined so as to minimize the value of A given by the equation (5) when the r_{min}, W_{total }and D are given.
The remainder of the configuration, functions and effects of this embodiment are the same as those of the fifth or sixth embodiment.
Now, explained below are an example of the planar coil according to the sixth embodiment (hereinafter referred to as a fifth working example) and an example of the planar coil according to the seventh embodiment (hereinafter referred to as a sixth working example), and the results of comparison of calculated resistance values between the planar coils of the working examples and a planar coil of a seventh comparative example.
For each of the planar coils of the fifth working example, the sixth working example and the seventh comparative example, copper was used as the conductor constituting the winding, thickness t of the conductor was set to 0.06 mm, the inner radius r_{min }of the innermost winding portion was set to 6.4 mm, a difference W_{total }between the outer radius of the outermost winding portion and the inner radius of the innermost winding portion was set to 5.1 mm, and a distance D between winding portions at adjacent turns was set to 0.2 mm. Under these conditions, values of the inner radius r_{i}(n) and the outer radius r_{o}(n) for a winding portion at each turn and a resistance value R_{total }of the entire winding were determined for each planar coil. The volume resistivity of the copper was set to 1.72×10^{−8 }(Ωm). The width r_{o}(n)−r_{i}(n) of a winding portion at each turn is hereinafter expressed as W(n).
For each of the planar coils of the fifth working example, the sixth working example and the seventh comparative example, the width W(n) of a winding portion at each turn and the resistance value R_{total }of the entire winding are as shown in the following table. In the table, the first conductor layer is referred to as “layer A” and the second conductor layer is referred to as “layer B.”
As can be seen from the table above, for the planar coil of the fifth working example, the resistance value R_{total }of the entire winding is reduced by 2.12% compared with the planar coil of the seventh comparative example. For the planar coil of the sixth working example, the resistance value R_{total }of the entire winding is reduced by 4.35% compared with the planar coil of the seventh comparative example. When the first and second patterned conductors each have winding portions of 2.5 turns to form a winding of five turns, the resistance value of the entire winding of the planar coil is equivalent to that of the seventh comparative example.
[Eighth Embodiment]
Reference is now made to FIG. 41 through
In the planar coil of the present embodiment, the insulating layer 40, the first conductor layer 41, and the second conductor layer 42 of the fourth or fifth embodiment are combined to make one set, and three sets of them are stacked in a direction of thickness, with the windings of the respective sets being connected in parallel to each other. The planar coil of the embodiment comprises a stacked body 50 made up of the stacked three sets of the insulating layer 40, the first conductor layer 41 and the second conductor layer 42, and Etype cores 51A and 51B attached to the stacked body 50.
As shown in FIG. 41 and
Additionally, as shown in
The remainder of the configuration, functions and effects of the present embodiment are the same as those of the fourth or fifth embodiment.
[Ninth Embodiment]
Reference is now made to
As an example of the planar coil of the present embodiment (hereinafter referred to as a seventh working example), a prototype planar coil was fabricated including the stacked body 50 formed by stacking three sets of the planar coil of the fifth working example, with the windings of the respective sets connected in parallel to each other. The resistance of the entire winding of the prototype planar coil of the seventh working example measured 15.05 mΩ.
As a comparative example (hereinafter referred to as an eighth comparative example) against the seventh working example, a prototype planar coil was fabricated including a stacked body 250 formed by stacking three sets of the planar coil of the seventh comparative example, with the windings of the respective sets connected in parallel to each other.
Thus, the rate of reduction in resistance of the planar coil of the seventh working example is 2.15% as compared with the planar coil of the eighth comparative example, which is equivalent to the rate of reduction in resistance of the planar coil of the fifth working example against the planar coil of the seventh comparative example.
The remainder of the configuration, functions and effects of the present embodiment are the same as those of the sixth, seventh, or eighth embodiment.
[Tenth Embodiment]
Now, description will be given of a configuration of a planar transformer according to a tenth embodiment of the invention.
As shown in FIG. 48 and
Additionally, as shown in
The stacked body 60 includes four types of conductor layers, i.e., a PA layer, a PB layer, an SA layer, and an SB layer, and the insulating layers 70. The four types of conductor layers each include a patterned conductor that is formed by arranging a platelike conductor, including a foillike conductor, into a flatspiral shape. The PA layer and the PB layer form the primary winding of five turns, while the SA layer and the SB layer form the secondary winding of two turns. Therefore, the planar transformer according to the embodiment has a turns ratio of 5:2.
As shown in
As shown in
As shown in
As shown in FIG. 53 and
As shown in
The PA layer, PB layer, SA layer and SB layer are stacked in the following order from the bottom: SA layerPA layerSB layerPB layerSA layerPA layerSB layerSA layerPB layerSB layerPA layerSA layerPB layerSB layer.
As an example of the planar transformer according to the present embodiment (hereinafter referred to as an eighth working example), a prototype planar transformer was fabricated in which the first patterned conductor 41a and the second patterned conductor 42a of the fifth working example were used for the PA layer and the PB layer, respectively, each insulating layer 70 was 0.1 mm in thickness, and the cores 51A and 51B were made of ferrite. In the prototype planar transformer of the eighth working example, the winding resistance at 200 kHz as viewed from the primary side measured 36.82 mΩ.
As a comparative example (hereinafter referred to as a ninth comparative example) against the eighth working example, a prototype planar transformer was fabricated including a stacked body 260 in which the first patterned conductor 141a and the second patterned conductor 142a of the seventh comparative example were used for the PA layer and the PB layer, respectively, and each insulating layer 70 was 0.1 mm in thickness, with the cores 51A and 51B made of ferrite.
Thus, as compared with the planar transformer of the ninth comparative example, the planar transformer of the eighth working example has attained a 2.6% reduction in the highfrequency resistance at 200 kHz.
In the present embodiment, the primary winding has an odd number of turns (five turns) and the secondary winding has an even number of turns (two turns). However, the primary winding may have an even number of turns and the secondary winding may have an odd number of turns. Alternatively, both the primary and secondary windings may have an odd number of turns.
The remainder of the configuration, functions and effects of the present embodiment are the same as those of the sixth or seventh embodiment.
In the fourth to tenth embodiments, the number of turns of the winding or the patterned conductors, and the number of the conductor layers can be set to any number.
Additionally, in the fourth to tenth embodiments, the winding may be formed of a conductor other than plateshaped ones, and more specifically, a rounded wire conductor, for example.
As described in the foregoing, according to the fourth to tenth embodiments, in the first and second patterned conductors each including winding portions of N+1 turns, the innermost winding portions of the first and second patterned conductors are connected in parallel to each other so as to form a winding of 2N+1 turns. Accordingly, in the fourth to tenth embodiments, the first patterned conductor and the second patterned conductor may be formed into the same pattern in terms of width. In the fourth to tenth embodiments, the conductive path corresponding to one turn that is formed by the innermost winding portions of the first and second patterned conductors is twice as thick as the other conductive path. However, by adjusting the width thereof, it is possible to reduce the resistance value of the entire winding of 2N+1 turns, and to thereby reduce a loss in the entire winding. From the foregoing, the fourth to tenth embodiments make it possible to achieve a reduction in thickness of the planar coil or the planar transformer, great flexibility in designing the number of conductor layers, and a reduction in loss.
In the fourth to tenth embodiments, the innermost winding portion of each of the first and second patterned conductors may have a width that is substantially half the width of another winding portion. In this case, it is possible to uniformalize a current density for every portion of the winding of 2N+1 turns, and as a result, it is possible to reduce a loss in the winding further.
In the fourth to tenth embodiments, for the first patterned conductor and the second patterned conductor, the r_{i}(n) and r_{o}(n) may be set so as to minimize the value of A given by the equation (5). In this case, it is possible to minimize the resistance value of the entire winding, and as a result, it is possible to minimize a loss in the entire winding.
It is apparent that the present invention may be carried out in various modes and may be modified in various manners based on the foregoing description. Therefore, within the scope of equivalence of the scope of the following claims, the invention may be practiced otherwise than as specifically described.
Claims
1. A planar coil comprising a winding formed by arranging a conductor into a flatspiral shape, the winding including winding portions of N turns (N is an integer greater than or equal to two), wherein:
 letting ri(n) be a radius of an inner circumference of a winding portion at the nth turn (n is an integer greater than or equal to one and less than or equal to N) from the inner side; ro(n) be a radius of an outer circumference of the same; rmin be a radius of an inner circumference of the innermost winding portion; Wtotal be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the ri(n) and ro(n) are determined so as to minimize a value of A expressed by equation (1) when the rmin, Wtotal and D are given: A = ∑ n = 1 N ( log r o ( n ) r i ( n ) )  1 ( 1 )
 where ri(1)=rmin, ri(n+1)−ro(n)=D, and ro(N)−ri(1)=Wtotal.
2. A planar coil according to claim 1, wherein a plurality of said windings are provided, and the plurality of said windings are stacked in a direction of thickness with an insulating layer disposed between adjacent ones, and are connected in parallel or in series to each other.
3. A planar transformer comprising a plurality of windings each formed into a flat shape and stacked in a direction of thickness, and an insulating layer disposed between adjacent ones of the windings, a part of the plurality of windings serving as a primary winding and another part of the plurality of windings serving as a secondary winding, wherein:
 at least one of the plurality of windings includes winding portions of N turns (N is an integer greater than or equal to two), the winding portions being formed by arranging a conductor into a flatspiral shape, and
 letting ri(n) be a radius of an inner circumference of a winding portion at the nth turn (n is an integer greater than or equal to one and less than or equal to N) from the inner side; ro(n) be a radius of an outer circumference of the same; rmin be a radius of an inner circumference of the innermost winding portion; Wtotal be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the ri(n) and ro(n) are determined so as to minimize a value of A expressed by equation (1) when the rmin, Wtotal and D are given: A = ∑ n = 1 N ( log r o ( n ) r i ( n ) )  1 ( 1 )
 where ri(1)=rmin, ri(n+1)−ro(n) D, and ro(N)−ri(1)=Wtotal.
4. A planar coil having a winding of an odd number of turns, the winding being formed of a conductor, the planar coil comprising: an insulating layer; a first conductor layer including a first patterned conductor formed by arranging a conductor into a flatspiral shape; and a second conductor including a second patterned conductor formed by arranging a conductor into a flatspiral shape, the second conductor layer being adjacent to the first conductor layer via the insulating layer, wherein:
 each of the first patterned conductor and the second patterned conductor includes a winding portion of an innermost one turn and the remaining winding portion of N (N is an integer greater than or equal to one) turns, and
 only the winding portion of the innermost one turn of the first patterned conductor and only the winding portion of the innermost one turn of the second patterned conductor are connected in parallel to each other, thereby allowing the first patterned conductor and the second patterned conductor to form the winding of 2N+1 turns.
5. A planar coil according to claim 4, wherein
 in each of the first patterned conductor and the second patterned conductor, the winding portion of the innermost one turn has a width that is substantially half the width of the remaining winding portion.
6. A planar coil according to claim 4, wherein
 in the first patterned conductor and the second patterned conductor, letting ri(n) be a radius of an inner circumference of a winding portion at the nth turn (n is an integer greater than or equal to 1 and less than or equal to N+1) from the inner side; ro(n) be a radius of an outer circumference of the same; rmin be a radius of an inner circumference of the innermost winding portion; Wtotal be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the ri(n) and ro(n) are determined so as to minimize a value of A expressed by equation (5) when the rmin, Wtotal and D are given: A = ∑ n = 1 N + 1 K ( n ) ( log r o ( n ) r i ( n ) )  1 ( 5 )
 where K(1)=0.5; K(n)=2 when n≧2; ri(1)=rmin; ri(n+1)−ro(n)=D; and ro(N+1)−ri(1)=Wtotal.
7. A planar coil according to claim 4, wherein a plurality of sets of the insulating layer, the first conductor layer and the second conductor layer are stacked in a direction of thickness, and the windings of the respective sets are connected in parallel to each other.
8. A planar transformer having a primary winding and a secondary winding, each being formed of a conductor arranged into a flat shape, wherein:
 at least one of the primary winding and the secondary winding comprises: a first conductor layer including a first patterned conductor formed by arranging a conductor into a flatspiral shape; and a second conductor including a second patterned conductor formed by arranging a conductor into a flatspiral shape, the second conductor layer being adjacent to the first conductor layer via an insulating layer,
 each of the first patterned conductor and the second patterned conductor includes a winding portion of an innermost one turn and the remaining winding portion of N (N is an integer greater than or equal to one) turns, and
 only the winding portion of the innermost one turn of the first patterned conductor and only the winding portion of the innermost one turn of the second patterned conductor are connected in parallel to each other, thereby allowing the first patterned conductor and the second patterned conductor to form a winding of 2N+1 turns.
9. A planar transformer according to claim 8, wherein
 in each of the first patterned conductor and the second patterned conductor, the winding portion of the innermost one turn has a width that is substantially half the width of the remaining winding portion.
10. A planar transformer according to claim 8, wherein
 in the first patterned conductor and the second patterned conductor, letting ri(n) be a radius of an inner circumference of a winding portion at the nth turn (n is an integer greater than or equal to 1 and less than or equal to N+1) from the inner side; ro(n) be a radius of an outer circumference of the same; rmin be a radius of an inner circumference of the innermost winding portion; Wtotal be a difference between a radius of an outer circumference of the outermost winding portion and the radius of the inner circumference of the innermost winding portion; and D be a distance between winding portions at adjacent turns, the ri(n) and ro(n) are determined so as to minimize a value of A expressed by equation (5) when the rmin, Wtotal and D are given: A = ∑ n = 1 N + 1 K ( n ) ( log r o ( n ) r i ( n ) )  1 ( 5 )
 where K(1)=0.5; K(n)=2 when n≧2; ri(1)=rmin; ri(n+1)−ro(n)=D; and ro(N+1)−ri(1)=Wtotal.
1 085 538  March 2001  EP 
A 4113605  April 1992  JP 
A 5226155  September 1993  JP 
A 737728  February 1995  JP 
A 10163039  June 1998  JP 
A 11307366  November 1999  JP 
A 200185230  March 2001  JP 
200185230  March 2001  JP 
Type: Grant
Filed: Feb 28, 2002
Date of Patent: Jan 25, 2005
Patent Publication Number: 20030179067
Assignee: TDK Corporation (Tokyo)
Inventors: Masahiro Gamou (Tokyo), Satoshi Horikami (Tokyo)
Primary Examiner: Lincoln Donovan
Assistant Examiner: Jennifer A. Poker
Attorney: Oliff & Berridge, PLC
Application Number: 10/297,801